Skip to main content

K-radical classes of lattice ordered groups

  • Partially Ordered Algebraic Structures
  • Conference paper
  • First Online:
Algebra Carbondale 1980

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 848))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Anderson, Subprojectable and locally flat lattice ordered groups, Dissertation, Kansas University (1977).

    Google Scholar 

  2. A. Bigard, Contribution a la theorie des groupes reticules, Thesis, University of Paris (1969).

    Google Scholar 

  3. R. Byrd, "Archimedean closures in lattice ordered groups," Canad. J. Math. 21 (1969) 1004–1011. (MR 39 #6804)

    Article  MathSciNet  MATH  Google Scholar 

  4. —, "Complete distributivity in lattice ordered groups," Pacific J. Math. 26 (1967) 423–432. (MR 34 #7680)

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Byrd and T. Lloyd, "Closed subgroups and complete distributivity in lattice ordered groups," Math. Zeitschr. 101 (1967) 123–130. (MR 36 #1371)

    Article  MathSciNet  MATH  Google Scholar 

  6. —, "Kernels in lattice ordered groups," Proc. Amer. Math. Soc. 57 (1976) 16–18. (MR 53 #10686)

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Bleier and P. Conrad, "The lattice of closed ideals and a*-extensions of an abelian l-group," Pacific J. Math. 47 (1973) 329–340. (MR 48 #3833)

    Article  MathSciNet  MATH  Google Scholar 

  8. —, "a*-closures of lattice ordered groups," Trans. Amer. Math. Soc. 209 (1975) 367–387. (MR 53 #7892)

    MathSciNet  MATH  Google Scholar 

  9. P. Conrad, "Some structure theorems for lattice ordered groups," Trans. Amer. Math. Soc. 99 (1961) 212–240. (MR 22 #12143)

    Article  MathSciNet  MATH  Google Scholar 

  10. —, J. Harvey and C. Holland, "The Hahn embedding theorem for abelian lattice ordered groups," Trans. Amer. Math. Soc. 108 (1963) 143–169. (MR 27 #1519)

    Article  MathSciNet  MATH  Google Scholar 

  11. —, "The relationship between the radical of a lattice ordered group and complete distributivity," Pacific J. Math. 14 (1964) 493–499. (MR 29 #3556)

    Article  MathSciNet  MATH  Google Scholar 

  12. —, "The lattice of all convex l-subgroups of a lattice ordered groups," Czech. Math. J. 15 (1965) 101–123. (MR 30 #3926)

    MathSciNet  MATH  Google Scholar 

  13. —, "Archimedean extensions of lattice-ordered groups," J. Indian Math. Soc. 30 (1966) 131–160. (MR 37 #118)

    MathSciNet  MATH  Google Scholar 

  14. —, "A characterization of lattice ordered groups by their convex l-subgroups," J. Australian Math. Soc. 7 (1967) 145–159, (MR 35 #5371)

    Article  MathSciNet  MATH  Google Scholar 

  15. —, "The lateral completion of a lattice ordered group," Proc. London Math. Soc. 19 (1969) 444–480. (MR 39 #5442)

    Article  MathSciNet  MATH  Google Scholar 

  16. —, "The essential closure of an archimedean lattice ordered group," Duke Math. J. 38 (1970) 151–160. (MR 43 #3190)

    Article  MathSciNet  MATH  Google Scholar 

  17. —, Lattice ordered groups, Lecture notes, Tulane Math. Library (1970).

    Google Scholar 

  18. —, "The hulls of representable l-groups and f-rings," J. Australian Math. Soc. 16 (1973) 385–415.

    Article  MathSciNet  MATH  Google Scholar 

  19. —, "Changing the scalar multiplication on a vector lattice," J. Australian Math. Soc. 20 (1975) 332–347. (MR 52 #13563)

    Article  MathSciNet  MATH  Google Scholar 

  20. —, "Torsion radicals of lattice ordered groups," Symposia Math. 21 Academic Press (1977) 479–513. (MR 57 #5885)

    MathSciNet  MATH  Google Scholar 

  21. —, "Minimal prime subgroups of lattice ordered groups," to appear.

    Google Scholar 

  22. —, "The structure of an l-group that is determined by its minimal prime subgroups," to appear.

    Google Scholar 

  23. A. Glass, C. Holland and S. McCleary, "a*-closures of completely distributive lattice ordered groups," Pacific J. Math. 59 (1975) 43–67. (MR 52 #7994)

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Jakubic, "Radical mappings and radical classes of lattice ordered groups," Symposia Math. Academic Press (1977) 451–477. (MR 58 #10653)

    Google Scholar 

  25. —, "Archimedean kernel of a lattice ordered group," Czech. Math. J. 28 (1978) 140–159.

    MathSciNet  Google Scholar 

  26. O Kenny, Lattice ordered groups, Dissertation, Kansas University (1975).

    Google Scholar 

  27. J. Martinez, "Torsion theory for lattice ordered groups," Czech. Math. J. 25 (1975) 284–298. (MR 52 #10537)

    MathSciNet  MATH  Google Scholar 

  28. —, The general theory of torsion classes for lattice ordered groups, Lecture notes.

    Google Scholar 

  29. S. McCleary, "The closed prime subgroups of certain ordered permutation groups," Pacific J. Math. 31 (1969) 745–754. (MR 42 #1736)

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Redfield, "Archimedean and basic elements in completely distributive lattice ordered groups," Pacific. J. Math. 63 (1976) 247–253.

    Article  MathSciNet  MATH  Google Scholar 

  31. S. Wolfenstein, Contribution a 1 etude des groups reticules, Thesis, University of Paris (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ralph K. Amayo

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Conrad, P. (1981). K-radical classes of lattice ordered groups. In: Amayo, R.K. (eds) Algebra Carbondale 1980. Lecture Notes in Mathematics, vol 848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090566

Download citation

  • DOI: https://doi.org/10.1007/BFb0090566

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10573-2

  • Online ISBN: 978-3-540-38549-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics